Two components operate in parallel in a device, so the device fails when and only when both

Question:

Two components operate in parallel in a device, so the device fails when and only when both components fail. The lifetimes, X1 and X2, of the respective components are independent and identically distributed with an exponential distribution with θ = 2. The cost of operating the device is Z = 2Y1 + Y2, where Y1 = min (X1, X2) and Y2 = max (X1, X2). Compute E(Z).

Distribution
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